arXiv subjects

Dipo Aldila

Publications and source records attributed to Dipo Aldila.

4 recordsLinked to original sources

arXiv2026

A Mathematical Model of Dengue Transmission Incorporating Hospital Capacity and Threshold-Based Fogging Interventions

Dengue remains a major public health challenge in tropical regions, and recurring outbreaks suggest that current intervention strategies are not yet fully effective. Existing mathematical models typically assume unlimited hospital capacity and continuously applied fogging, neglecting practical constraints that strongly influence disease control. We develop a non-smooth ordinary differential equation model of dengue transmission that incorporates finite hospital capacity and a threshold-triggered fogging strategy activated when reported infections exceed a prescribed fraction of the available capacity. The model exhibits three epidemiologically relevant operating regimes, reflecting changes in hospitalization and vector-control policies as the epidemic progresses. We establish the existence and local stability of the disease-free and endemic equilibria. Numerical continuation confirms the analytical results and reveals boundary-equilibrium bifurcations at the switching thresholds, a Hopf bifurcation after hospital capacity is exceeded leading to sustained oscillatory outbreaks, and a fold bifurcation near the epidemic threshold that generates additional unstable equilibria. We further investigate periodic solutions with respect to the fogging rate and activation threshold, identifying locally optimal intervention regimes that reduce epidemic peaks while avoiding unnecessarily intensive control efforts. The results demonstrate that hospital capacity, reactive fogging, and intervention thresholds fundamentally shape dengue dynamics and provide quantitative insights for designing effective state-dependent control strategies under limited healthcare resources.

math.DS↗

arXiv2020

An epidemic model highlighting humane social awareness and vector-host lifespan ratio variation

Many vector-borne disease epidemic models neglect the fact that in modern human civilization, social awareness as well as self-defence system are overwhelming against advanced propagation of the disease. News are becoming more effortlessly accessible through social media and mobile apps, while apparatuses for disease prevention are inclined to be more abundant and affordable. Here we study a simple host-vector model in which media-triggered social awareness and seasonality in vector breeding are taken into account. There appears a certain threshold indicating the alarming outbreak; the number of infective human individuals above which shall actuate the self-defence system for the susceptible subpopulation. A model where the infection rate revolves in the likelihood of poverty, reluctancy, tiresomeness, perceiving the disease as being easily curable, absence of medical access, and overwhelming hungrier vectors is proposed. Further discoveries are made from undertaking disparate time scales between human and vector population dynamics. The resulting slow-fast system discloses notable dynamics in which solution trajectories confine to the slow manifold and critical manifold, before finally ending up at equilibria. How coinciding the slow manifold with the critical manifold enhances periodic forcing is also studied. The finding on hysteresis loops gives insights of how defining alarming outbreak critically perturbs the basic reproductive number, which later helps keep the incidence cycle on small magnitudes.

q-bio.PE↗

arXiv2017

Learning the seasonality of disease incidences from empirical data

Investigating the seasonality of disease incidences is very important in disease surveillance in regions with periodical climatic patterns. In lieu of the paradigm about disease incidences varying seasonally in line with meteorology, this work seeks to determine how well standard epidemic models can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the disease occurrences can be performed using the classical Floquet theory, which explains the stability of the existing periodic solutions. For a test case, we employed an IR model to assimilate weekly dengue incidence data from the city of Jakarta, Indonesia, which we present in their raw and moving-average-filtered versions. To estimate a periodic parameter toward performing the asymptotic analysis, eight optimization schemes were assigned returning magnitudes of the parameter that vary insignificantly across schemes. Furthermore, the computation results combined with the analytical results indicate that if the disease surveillance in the city does not improve, then the incidence will raise to a certain positive orbit and remain cyclical.

math.OC↗

arXiv2017

Analysis of a network--based SIR model

This study focuses on analyzing a deterministic SIR model governing the dynamics of the hosts and vectors on an urban network. Our analysis scrutinizes the typical existence--stability of the equilibria as well as the sensitivity of the basic reproductive number. The latter is a groundbreaking finding that has a strong applicative relevance, particularly for addressing the problem of the distribution of job opportunities toward diminishing the disease persistence on the entire network.

math.DS↗